i dont understand the step accompanied to the one i marked...i quite dont understand !

If you relate summation(r= 1 to 10) ¹⁰C_10-r . ²⁰C_r with the concepts from permutation and combination, Then we can say that this term represent, chossing 10 objects out of 30 in which 10 are of one type and 20 are of another type.
So directly we can write these as ³⁰C₁₀ but we are subtracting -1 because r starts from 1 not 0. Which means that all 10 can not be of one from the first 10 similar objects.

And same about the next term also.

Thanks.

Approved